If my math is right...it will have an effect of approximately 0.0000000001 g

Angular acceleration is r*w^2, so for a normal day that would be 6371000*(2*pi/86400)^2/g = 0.0034345580g

On this accelerated day, it becomes 6371000*(2*pi/86399.9987)^2/g = 0.0034345581g

That's at the equator assuming a radius of 6371 km, which is a decent ballpark, the specific number won't change the result much.